Anomocora Studer, 1878 (basis of record)
Anomocora fecunda (Pourtalès, 1871) (basis of record)
Astrangia Milne Edwards & Haime, 1848 (basis of record)
Balanophyllia Wood, 1844 (basis of record)
Caryophyllia Lamarck, 1801 (basis of record)
Caryophylliidae Dana, 1846 (basis of record)
Cladocora Ehrenberg, 1834 (basis of record)
Cladocora caespitosa (Linnaeus, 1767) (basis of record)
Cladopsammia Lacaze-Duthiers, 1897 (basis of record)
Dasmosmilia Pourtalès, 1880 (basis of record)
Deltocyathoides Yabe & Eguchi, 1932 accepted as Peponocyathus Gravier, 1915 (basis of record)
Deltocyathus Milne Edwards & Haime, 1848 (basis of record)
Dendrophyllia de Blainville, 1830 (basis of record)
Dendrophyllia cornigera (Lamarck, 1816) (basis of record)
Dendrophyllia ramea (Linnaeus, 1758) (basis of record)
Dendrophylliidae Gray, 1847 (basis of record)
Eguchipsammia Cairns, 1994 (basis of record)
Eguchipsammia gaditana (Duncan, 1873) (basis of record)
Flabellidae Bourne, 1905 (basis of record)
Flabellum Lesson, 1831 (basis of record)
Guyniidae Hickson, 1910 (basis of record)
Javania Duncan, 1876 (basis of record)
Madracis Milne Edwards & Haime, 1849 (basis of record)
Madrepora Linnaeus, 1758 (basis of record)
Monomyces Ehrenberg, 1834 (basis of record)
Oculina Lamarck, 1816 (basis of record)
Oculina patagonica de Angelis D'Ossat, 1908 (basis of record)
Oculinidae Gray, 1847 (basis of record)
Paracyathus Milne Edwards & Haime, 1848 (basis of record)
Peponocyathus Gravier, 1915 (basis of record)
Pocilloporidae Gray, 1840 (basis of record)
Polycyathus Duncan, 1876 (basis of record)
Rhizangiidae d'Orbigny, 1851 (basis of record)
Solenosmilia Duncan, 1873 (basis of record)
Solenosmilia variabilis Duncan, 1873 (basis of record)
Sphenotrochus Milne Edwards & Haime, 1848 (basis of record)
Stenocyathus Pourtalès, 1871 (basis of record)
Tethocyathus Kühn, 1933 (basis of record)
Trochocyathus Milne Edwards & Haime, 1848 (basis of record)
Turbinoliidae Milne Edwards & Haime, 1848 (basis of record)